Nuprl - Proof: composite with prime factor 1 1 1 1 2

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At: composite with prime factor 1 1 1 1 2

1. x :

x1:

. x1<x

prime(x1)

(

i,j:{2..x1

}. x1 = i

j & prime(i))
3. 2

x
4.

prime(x)
5. i : {2..x

}
6. j : {2..x

}
7. x = i

j
8.

prime(i)

i,j:{2..x

}. x = i

j & prime(i)

By:	Inst: Hyp:2 Using:[i] ... THEN CBV-1: n:<type>, m:<type>. <prop> THEN ExistHD Hyp:-1

Generated subgoal:

1 9. n : {2..i}
10. m : {2..i}
11. i = nm
12. prime(n)
i,j:{2..x}. x = ij & prime(i)
7 steps

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